If the temperature difference on the two sides of a wall increases from `100^@C` to `200^@C`, its thermal conductivity

Options

A. remains unchanged
B. is doubled
C. is halved
D. become four times

Explanation

To solve the problem, we need to analyze the relationship between temperature difference and thermal conductivity. The question states that the temperature difference across a wall increases from \(100^\circ C\) to \(200^\circ C\), and we need to determine how this affects the thermal conductivity of the wall.

### Step-by-Step Solution:

1. **Understand the Concept of Thermal Conductivity**:
Thermal conductivity (\(k\)) is a property of the material that indicates its ability to conduct heat. It is defined as the amount of heat (\(Q\)) conducted per unit time (\(t\)) through a unit area (\(A\)) of the material for a unit temperature difference (\(\Delta T\)).

2. **Use Fourier's Law of Heat Conduction**:
According to Fourier's law, the rate of heat transfer (\(\frac{dQ}{dt}\)) through a material is given by:
\[ \frac{dQ}{dt} = -k \cdot A \cdot \frac{\Delta T}{\Delta x} \]
where:
- \(k\) = thermal conductivity
- \(A\) = area through which heat is being transferred
- \(\Delta T\) = temperature difference across the material
- \(\Delta x\) = thickness of the material

3. **Analyze the Given Temperature Difference**:
The problem states that the temperature difference (\(\Delta T\)) increases from \(100^\circ C\) to \(200^\circ C\). However, thermal conductivity (\(k\)) is a material property and does not depend on the temperature difference.

4. **Conclusion about Thermal Conductivity**:
Since thermal conductivity is a characteristic of the material and does not change with temperature difference, we conclude that the thermal conductivity remains unchanged even when the temperature difference increases from \(100^\circ C\) to \(200^\circ C\).

5. **Final Answer**:
Therefore, the thermal conductivity of the wall remains unchanged.